We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Rota–Baxter cosystems and coquasitriangular mixed bialgebras.
- Authors
Ma, Tianshui; Makhlouf, Abdenacer; Silvestrov, Sergei
- Abstract
In this paper, we present a dual version of T. Brzeziński's results about Rota–Baxter systems which appeared in [Rota–Baxter systems, dendriform algebras and covariant bialgebras, J. Algebra460 (2016) 1–25]. Then as a generalization to bialgebras, we introduce the notion of Rota–Baxter bisystem and construct various examples of Rota–Baxter bialgebras and bisystems in dimensions 2, 3 and 4. On the other hand, we introduce a new type of bialgebras (named mixed bialgebras) which consist of an associative algebra and a coassociative coalgebra satisfying the compatible condition determined by two coderivations. We investigate coquasitriangular mixed bialgebras and the particular case of coquasitriangular infinitesimal bialgebras, where we give the double construction. Also, we show in some cases that Rota–Baxter cosystems can be obtained from a coquasitriangular mixed bialgebras.
- Subjects
YANG-Baxter equation; DIMENSION theory (Algebra); GENERALIZATION
- Publication
Journal of Algebra & Its Applications, 2021, Vol 20, Issue 04, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949882150064X